Joist selection

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Well, if I did the integrations correctly, the moment of inertia I_x of a 4x8 missing the upper right quadrant is 22/15 times that of a 2x8. I'm a little surprised that the ratio wasn't smaller. I'm still not sure if it is worth the trouble, but it is an interesting exercise.

Yeah, it's the glue part that gives me pause, the old 2x4s are quite rough, so I'd need a special glue that can gap fill, which seems like a lot of trouble.
Cheers, Wayne
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Wayne-
I didn't understand your ratio thing....are you saying that the 2x8 with a 2x4 attached (nailed or glued) is ~1.4 times stiffer than a 2x8 alone? The 22/15 ratio was a little obscure

a heavy spread of wood glue should easily fill surface of the old 2x4's or use a construction adhesive....adhesives are much better for shear transfer than mechanical fasteners
by sistering the 2x8 to the 2x4 you'll reduce the deflection to 68% of the deflection of the 2x8 alone.....so it wll go from 1/2" to ~3/8"
cheers Bob
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Yes. That's for a 2" x 3.625" 2x4, which is what I have. So the section ends up being 3.5" x 7.25" (a 4x8) minus one quadrant.

But wood glue isn't gap filling, is it?
Thanks, Wayne
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Depends on what sort of wood glue you're talking about. If you're talking about Elmer's PVA, no, but if you're talking about construction adhesive marketed for specific applications, like Liquid Nails, or the PL brand of adhesives, they will work fine for you application.
It seems to me that you're overanalyzing this thing. Two pieces of wood have been attached with nails in shear for centuries with no adhesive at all. Balloon framed houses used a ribbon/ledger to support the floor joists with both being attached to the full height studs with nails in shear only. They're not falling down. Your house is from 1908 - prime balloon framing period. Is that how your floor joists are connected?
Your low height attic load is far less and you're analyzing it far more. And you'd already determined that the 2x8 on it's own would take care of the load - it doesn't need the sistered 2x4 to do the work, so the nails in shear won't be doing a hell of a lot of work. The glue question is like a guy wearing a belt and suspenders asking if he needs overalls to keep his pants up.
The only small wrinkle was the 1x4 plate resting on top of the CJs requiring the notch. You'd already established that shear and bearing area weren't issues as a single 2x6 was adequate. Since you will have double the sectional area there's really no question of the notch being a problem. In balloon framed houses it's not uncommon to have a flush beam or two supporting the inboard ends of the first floor joists. The standard way of doing that, before the introduction of joist hangers, was to nail a 2x3 ledger flat to the side, and flush with the bottom of the flush beam. The FJs were notched to rest on the ledger and toe-nailed to the beam. The notch on the bottom is a _much_ bigger issue than a notch on the top, yet even though you'll often see splits at the notch when you dissect the house, you rarely see failures.
My concern with the deflection is due to the fact that I don't consider 1/360 adequate for a floor. That's code - code is the minimum acceptable - I don't build that way. People also don't _live_ that way - particularly not with attics. A live load of 30 PSF in a bedroom is reasonable. People need to move around in a bedroom, and they don't pile stuff on every square foot of available floor space. That's not the case for an attic.
It wasn't clear from your earlier posts exactly how much room (height and area) is in the attic, and it wasn't clear what would be stored there. A single liquor bottle size box of books can weigh more than 20 PSF, and, if there's room, people stack stuff in an attic. If you can guarantee that the attic will never see more than the 20 PSF, even after you sell the house or kick the bucket, then fine - otherwise, go with a more conservative load and a more stringent deflection criteria.
As an aside, we could have gotten to the meat of the matter a lot more quickly if you'd posted a picture of the situation and/or given more complete information upfront.
Note to BobK: You said nails weren't good in shear. What does that mean? I had a building inspector say the same thing to me - I didn't want to argue with him just because he was wrong - he's the building inspector and the nails in shear wasn't an issue. You I can argue with! ;) What's your argument against nails in shear?
Okay, that's all for now. I'm hungry and I'm not going to proof read - let me know if any inanity worked it's way in. ;)
R
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Well, I think I narrowly framed my original question (double 2x6s or notched 2x8s), and we pretty quickly got to the practical answer (use tapered 2x8s). However, people were interested in the whole story, so I've been happy to provide the extra details. That has led to some interesting side questions, which are perhaps less practical.

No, it's platform framed. The only weird detail is the 1x4 plate between the ceiling joists and the rafters.

Just to be clear, I won't have double the sectional area. I'll have the sectional area of a 2x6 after I do the tapering. If I want to sister the existing 2x4s and consider its sectional area, then I have to be concerned with the sistering details. But since even the single 2x6 is deflection controlled, there is "reserve" sectional area there, so I'm not concerned about the possiblity of stress concentration from the tapering.

So what do you consider adequate? Will my skim coat plaster ceiling crack under a live load deflection of L/360?

The roof is hipped at an 8:12 slope, so over the 8' region, the clearance at center span varies from 0' to 5'4" or so. I'm not actually storing anything up there, my real concern is about the deflection from a person standing (squatting) on a single joist. As for others storing stuff up there, I guess that's why the building code requires a 20psf live load where the clearance exceeds 3'6". I think that's adequate in this situation.

I don't know about that, the meat of the matter from my point of view was in my original question, that's why I specifically made it as short and constrained as possible.
Above all, I appreciate the time and attention shown in your responses, they reflect the practical experience that I lack.
Thanks, Wayne
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The 'extra' details are usually the things that determine the best solution. There seems to be a bell curve to newsgroup questions. Newbies leave out all the pertinent information, then have to fill it in when people point the necessity of the omitted information. Posters with a bit more posting experience, but maybe not more technical information/experience, post more information up front. Posters with more technical experience often try to simplify the question to the one issue that concerns them. This leads back to the 'insufficient information for meaningful response' replies.

That was the low blood sugar talking. Sorry about that. Should have said _almost_ double the cross section. I don't any practical advantage to the tapering in your particular situation. This is what BobK wrote in his first reply: "You might consider a taper cut rather than a sharp cut out.
Timber is happier if you avoid abrupt section changes but in this case the local stress state appears to "compress" :notch rather than wanting to split it open."
I agree with the second part of the last sentence, and the _generality_ of the first part. Your situation won't benefit from tapering. It won't change any stress state. The same way doctors are supposed to "first, do no harm", carpenters are supposed to "not remove any wood without a reason." In your specific situation there is not reason to do it, so why do you want to do it? You should listen to BobK. ;)

Eventually. They all do. I don't think you're taking a big risk, and frankly if you're not storing anything up there you're not taking any risk at all. You could do me a favor though. After the supplemental CJs are in place, take an elevation of the bottom of a central joist at midspan. After you have rocked and plastered, do it again. I'm curious to see what sort of deflection you get from just the dead load.

For you, yes, I agree. Do not doubt that someone will do something stupid in that attic in years to come.

And therein lies the rub. You were able to inspect the situation firsthand and have way more information to help make a decision. Playing detective requires me to ask questions - some of which will be dead ends. I still have to ask them. The more experience I get the more finely tuned my analytical skills become. These newsgroups help me develop those skills and hopefully save somebody a 'learning' experience.

Hey, don't mention it. It's fun batting these things back and forth.
R
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OK, that is what I was trying to do, sorry if I wasn't successful in simplifying away the extraneous details while still providing the necessary details.

After thinking about it, I believe there will be a benefit as far as installing the new joists. Since they will have to fit between the wall top plate and the rafter 1x4 plate on both ends, I believe I'll have to put them in place flat, one end at a time, and then turn them upright. That would be hard to do if they are notched to fit tightly between the two plates. With a taper, the interference will be confined to a fraction of the thickness of the wall. Of course, that still may make it difficult. :-)

The weight of the 1/2" gypsum board is 2 psf, and I believe 1 psf would be generous for the skim coat plaster. So at 3 psf, the calculated deflection is 3/20 * 0.5" = 0.075", or 0.05" if I succesfully sister the existing joists. As to measuring it, that might take me six months, so we'll both have probably forgotten by then. :-)

Well, there's a limit to what I can do. It seems like it would be fair to match the stiffness of the ceiling joists before I removed the wall, and the stiffness of the ceiling joists in the rest of the attic. A quick check shows that both of these are/were at about L/360 deflection for 20psf live load, which is what I'll be providing.
Cheers, Wayne
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I'm not BobK, but I took this comment to mean that nails are not as good as adhesive when you want continuous shear transfer. And that you need continuous shear transfer to make the pieces of a built up beam act as a composite section. That's a different story than nailing a ledger to a stud wall, where the members are only overlapping in a small area.
Cheers, Wayne
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Wayne-
You're not me, you should thank goodness for that :)
but your answer

good as adhesive when you want continuous shear transfer. And that you need continuous shear transfer to make the pieces of a built up beam act as a composite section. That's a different story than nailing a ledger to a stud wall, where the members are only overlapping in a small area. <
was spot on to what I would have written
R-
I checked my posts & didn't find a direct reference to nails in shear being "not good"
but if I did, I was / am wrong.
Nails are fine in shear, I have no argument with nails in shear, that's what they're meant for (just not for withdrawal) I have no idea what that building inspector was thinking... ?????
but where one needs continuous shear transfer to develop composite action (built up box beam, I beam, etc) adhesives are much better than discrete mechanical fasteners because the stress is well distributed and the shear connection is stiffer than nails.........but since I often do "belt, suspenders, staples & duct tape"....... I prefer adhesive AND fasteners. :)
Also.guilty........Wayne & I tend to over analyze things
(him more than me, because he has less experience but he CAN do thecalcs & ask lots of questions...me, because I'm always looking for "better / optimum".
cheers Bob
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And why exactly do you need the shear transfer in your situation? You don't. You've already established that the new framing members can take the load on their own. There's little reason to tie the new CJs to the old so you don't really need adhesive, or nails for that matter.

But you don't need the existing 2x4s, so there is no reason to be concerned about shear transfer, right? Stiffness attracts load, and the 2x6s or 2x8 will be far stiffer than the existing 2x4. The 2x4, if sistered, won't be called on to do any work until the 2x8 has deflected enough that the 2x4 becomes involved, and that won't happen with a 1/2" deflection over a 17' span.

This is where theory and reality vary. I have no argument that two structural members that are attached continuously and not at isolated points, will do a better job in shear transfer. But there have been bolted and nailed composite beams in use for a long time - they're not failing.
So what does the adhesive add in this situation? Expense and time wasted. If the beam was in a more critical location, I'd agree with the belt and suspenders approach. In this specific situation there is absolutely nothing gained.

Me neither! He's a nice guy, though, so I let him slide. Interesting thing about his building department though - they had a big scandal a little while back. Four separate guys got busted for shady dealings - one of them was the commissioner. None of the guys knew what the other ones were doing. One guy, and you'll love this, refused to inspect/approve a homeowner's drywell installation until the homeowner bought four tickets to some firemen's benefit dinner! WTF?! So, for $900 or whatever it was - money he never saw, this guy threw away his career and is facing potential jail time.

Better/optimum also takes into account expense, effort and added benefit. I fail to see how construction adhesive affects any of those criteria in a positive way in Wayne's situation. If you just want to say, 'But it makes me _feel_ better!', then I wouldn't argue.
R
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OK, we have that the new 2x8 joist alone is deflection critical but adequate for the 16'5" span. Some have suggested that the 1/2" deflection this gives under live load is too much for that span. :-) So the question was raised of how to use the existing 2x4 joist to stiffen the new 2x8 joist. A few comments:
First, you statement "stiffness attracts load" is true when members are acting compatibly (same deflection) but separately. This would apply if the 2x4s are left in place, unattached to the 2x8s, and we considered that the gypsum board was sufficient to give equal deflections.
In this case, the moment of inertia (b*h^3/12) of the 2x8 (at 1.5" by 7.25") is six times that of the 2x4 (at 2" by 3.625"). So the overall system stiffness is 1 + 1/6 = 7/6 = 1.16 times as much as the 2x8 alone.
However, if we adequately tie the 2x4 to the side of the 2x8 (bottoms flush), such as by using frequent smaller nails, or a good adhesive, then the two members will act together as a composite section. This composite section, from the previous discussion, will be 22/15 = 1.47 times as stiff as the 2x8 alone.
This difference arises because the two members are different heights, and we are attaching them off center. In the more typical situation of both members being the same height, (a 2x8 sistered to a 2x8), the two calculations would give the same answer (twice as stiff). This is behind your experience that sistering without adhesive works fine. Similarly, if the 2x4 were attached to the 2x8 so their centerlines were at the same height, then again both calculations would give the same answer (1.16 times as stiff).
Lastly, as to the question of adhesive versus many small nails, I have the recollection that under load the nails will have an initial nail slip before being full engaged, while the adhesive won't have this initial slip. So in a deflection critical situation, the adhesive will work better. If the sistering is to increase strength, and the fastening is just to share the load, the difference is not important. I'm not 100% sure my recollection here is correct, perhaps BobK can confirm this.
Cheers, Wayne
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Wayne-
Thanks for posting this...my PC is acting up & I've lost a couple post before I sent them.
I hope you're not making Rico's head hurt with those numbers, mine is hurting :)
Be careful your post are starting to look a little like Nick's from Villanova. :)
You're spot on about sistering vs composite beam construction....we're talking about making an asymmetric T - beam.
In a true sistering situation a handful of nails & you're good to go.
In your situation we really want the 2x8 & the 2x4 to act as if they're the same piece of timber. If my memory serves me you need something like 100 psi or more in wood to get that behavior...pretty hard to do with nails.
btw when I retrofitted my attic joists (2x4's) I glued (epoxy) & osb cleated members onto the top edges of the existing 2x4's to create ~2x8's
I did this crazy thing because I had used redwood 2x6's leftover from a job from 10 years ago. The glued "top sistered" joists were stiffer than the 2x6's & I saved 2" of attic headroom that was critical.
I glued (brushed clean, no clamping, no cleats) test members together & tested them to failure. Glue stress at failure 173 psi shear.
Based on my calcs & testing the attic joists are ~6x stiffer now & can easily handle an attic storage load. :)
cheers Bob
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Wayne Whitney wrote:

You might want to think about your plasterboard layout and where you will have seems it'd be a good idea to glue and nail the sisters just to make sure there is no movement.
The rest I would just nail in place. Glue is a waste of time, IMO.
--
Art

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Creating a composite beam out of the 2x8 & 2x4 combo (with glue & nails) increases his joist stiffness by 50% which goes in the direction that you suggested....L/360 may not be stiff enough, L/520 is better.
Since his ceiling is unloaded....if he creates this composite asymmetric T beam he will get the added stiffness benefit. ....and his plaster may have a better chance of survival.
IMO a 50% increase in stiffness is worth the extra work (if you really think that L/360 is too limp then you should also agree that a 50% stiffness boost is worth it)
BTW tapers are elegant,
notches, esp when the kerfs intersect or they're made with saw & rigging axe
are ugly...... :)
cheers Bob
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Whoops, that's not quite right. The section is 1.5" x 7.25" plus 2" x 3.625". That section has a moment of inertia that is 22/15 times the moment of inertia of the simple 1.5" x 7.25" rectangle.
Wayne
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Wayne-
Your 22/15 ratio is making this old engineer crazier than I normally am.
A simple "factor of 1.5x stiffer" would be be easier for us practical types to parse.
That said, yeah, the sistering is a little more work
but with caulk tube dispensed adhesive, some set up clamps, shoot a bunch of staples or brads, remove the clamps & move to the next joist. You've only got five joists to do.....
"cost of quality vs cost of non-conformance"
how upset will you be when the ceiling finish cracks?
your 2x8 is deflection controlled, you've got lots of strength but the plaster finish wants stiffness........ you'll get L/520 instead of L/ 360
If you really want to "geek out" ....check the joist slope as a function of span for your assumed loading condition & compare to suggested limits for brittle finishes.
it's not really deflection that matters but changes in deflections
cheers Bob
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OK, I'm a mathematician, but when I'm doing engineering, you are right, I should say 1.5 because that easier to understand and 1.5 22/15 within the accuracy of our modeling of reality. :-)

I feel like I'll have to shoot at least 0.131" nails. I mean, I don't think the prescriptive building code recognizes construction adhesive as a substitute for nails?
BTW, is it fair to say that the adhesive connection is stiffer than the nail connection because the nail connection has an initial slip/crushing before it gets fully engaged?
Cheers, Wayne
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Wayne-
I was just kidding you....I know your the mathematician. :)
Those ratios make my head hurt...I think in factors & %'s.
Rico's hammering us (& rightfully so) ..........are we really adding any real performance benefit if you sister the old 2x4's to the new 2x8's? Yeah, the composite will be 50% stiffer, but do you need it?
In another post you state that the new 2x8's are stiffer than the old in place unmodified 2x6's. If that's so then you really don't need to add the extra stiffness beyond the new 2x8's
But
if the old 2x6's are stiffer than L/360 & the new 2x8's are stiffer than L/360
BUT if the new 2x8's are less stiff than the old 2x6's ........you'd be reducing the framing stiffness & the plaster MIGHT be unhappy.
In another post you state....

deflection for 20psf live load, which is what I'll be providing. <<<
you'll be fine as long as your new installation in reality is at least as stiff as the old one.
Another thing to consider, old growth DF has a higher elastic modulus than currently available new timbers. I sat on a committee with a REALLY old engineer (old enough to be my dad) & he'd sometimes spec the number of growth rings per inch on bending members!
Your comment about nail size.....I like smaller nails, they damage the wood less than larger nails. In fact .148 is about the largest nail I use unless I'm using VERY large timbers. Based on my research . 148 is about the largest nail that 2x's & 4's will accept without damaging trauma to the wood. I've tested lots of timber connections & large nails too close together (code allowed spacing is often too close) will create a connection that is weaker than smaller nails.
Additionally since this composite joist exercise is really above & beyond the code (you've already exceeded code min with the 2x8, right?) you can do whatever you want. Yeah, .113's are a good choice for "stitching" but I prefer a LOT of smaller fasteners.......an infinite number of infinitesimally small fasteners would approach the behavior of adhesive :)
My fastener of choice is a 16ga staple or 16ga brad but the .113 is ok too.

connection because the nail connection has an initial slip/crushing before it gets fully engaged? <<
Yup, that's why I prefer smaller fasteners & more of them. Smaller fasteners have smaller localized loads on the timber. 16 gage staples are good for ~250 lbs (per staple, ultimate shear failure load...lots of slip. They have effectively zero slip at 50 lbs per staple)
Nails have slip, glue doesn't; glue can be brittle & can fail, nailed connections are ductile & typically do not fail....that's why I combine them.
cheers Bob
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Rico needs it, as he says L/360 isn't stiff enough. :-) Based on the discussion I see it as a small definite improvement, when the time comes next week I'll figure out if it is worth the small definite extra work.

Yes, that's a good thing, as the old growth DF is #2 or #3, while the new members will be SS, so we can call it a wash. :-) Actually it's not really a wash, as a few of the old joists have large knots on the bottom half near midspan, that's really bad.

Assuming the old and new have the same E = 1.9 Mpsi and a 20psf live load and 10psf dead load, the old 2x6s spanned 13'9" (good for 14'4" at L/360 deflection) and the old 2x4s spanned 9' (good for 9'1" at L/360). The new 2x8s will span 16'5" (good for 17'2" at L/360). Everything is deflection controlled. So the new 2x8s will be just about as stiff as the old construction.

Good point.
Cheers, Wayne
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Wayne-
Is the E for new growth DF really 1.9 Mpsi?
btw correct me if the NDS says (or you if know) but SS is about flaws not a high E.
Old growth DF has very closely spaced growth rings & I was told that wood density drives E not knots / flaws.
I'd bet on the E of the old timber being higher but the new SS having few / no flaws.
Have you considered engineered timber? It can have some pretty high E's.
cheers Bob
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